\subsection{QRNoShifts}
\begin{simplechar}
\begin{lstlisting}
function [eigenValues, whichIterationAreWeOn, Matrix] = QRNoShifts(Matrix)

    [whichIterationAreWeOn, threshold, startingMatrix, matlabEigen] = initializeValues(Matrix);
    [Matrix, whichIterationAreWeOn] = QRNoShiftsLoop(threshold, Matrix, whichIterationAreWeOn);
    eigenValues = diag(Matrix)';
    displayResults(eigenValues, whichIterationAreWeOn, Matrix, startingMatrix, matlabEigen);
end
\end{lstlisting}
\end{simplechar}

\newpage
\subsubsection{QRNoShiftsLoop}
\begin{simplechar}
\begin{lstlisting}
function [Matrix, whichIterationAreWeOn] = QRNoShiftsLoop(threshold, Matrix, whichIterationAreWeOn)
    while threshold > 1e-6
        [Matrix, whichIterationAreWeOn, threshold] = QRNoShiftsInsideLoop(Matrix, whichIterationAreWeOn);
    end
end
\end{lstlisting}
\end{simplechar}

\subsubsection{QRNoShiftsInsideLoop}
\begin{simplechar}
\begin{lstlisting}
function [Matrix, whichIterationAreWeOn, threshold] = QRNoShiftsInsideLoop(Matrix, whichIterationAreWeOn)
    [Q, R] = gramSchmidtAlgorithm(Matrix);
    Matrix = R * Q;
    whichIterationAreWeOn = whichIterationAreWeOn + 1;

    % iterate until all non-diagonal elements are below the threshold
    matrixWithoutDiagonal = Matrix - diag(diag(Matrix)); % first diag converts Matrix
    % into vector consisting of values on the diagonal of matrix,
    % second diag converts this vector into matrix with zeros on
    % everything except diagonal
    % If we substract it from Matrix we get original Matrix with zeros
    % on a diagonal
    threshold = max(max(abs(matrixWithoutDiagonal)));
    % first max returns vector of elements
    % second max returns max element from this vector
end
\end{lstlisting}
\end{simplechar}

\newpage
\subsubsection{displayResults}
\begin{simplechar}
\begin{lstlisting}
function displayResults(eigenValues, whichIterationsAreWeOn, Matrix, startingMatrix, matlabEigen)
    disp("How many iterations it took:")
    disp(whichIterationsAreWeOn)
    disp("Starting Matrix:")
    disp(startingMatrix)
    disp("Final Matrix:")
    disp(Matrix)
    disp("eig(Matrix) eigen values:")
    disp(matlabEigen)
    disp("Our eigen values:")
    disp(eigenValues);
end
\end{lstlisting}
\end{simplechar}

\subsubsection{initializeValues}
\begin{simplechar}
\begin{lstlisting}
function [whichIterationAreWeOn, threshold, startingMatrix, matlabEigen] = initializeValues(Matrix)
    whichIterationAreWeOn = 0;
    threshold = inf;
    startingMatrix = Matrix;
    matlabEigen = eig(Matrix);
end
\end{lstlisting}
\end{simplechar}

\newpage